In this book, time
is always in physical units of seconds
(s), while time
or
is in units of samples (counting
numbers having no physical units). Time
is a continuous real
variable, while discrete-time in samples is integer-valued. The
physical time
corresponding to time
in samples is given by

For frequencies, we have two physical units: (1)
cycles per second and (2) radians per second. The
name for cycles per second is Hertz (Hz) (though in the past it
was cps). One cycle equals
radians, which is 360
degrees (). Therefore,
Hz is the same frequency as
radians per second (rad/s). It is easy to confuse the two because
both radians and cycles are pure numbers, so that both types of
frequency are in physical units of inverse seconds (s
).

Since the sampling period
is in seconds, the sampling rate
is in Hz. It can be helpful, however, to think ``seconds
per sample'' and ``samples per second,'' where ``samples'' is a
dimensionless quantity (pure number) included for clarity. The
amplitude of a signal may be in any arbitrary units such as
volts, sound pressure (SPL), and so on.